IAT (IISER) 2022

Organisms in which of the following phyla are triploblastic, acoelomate and have bilateral symmetry?

As opposed to DNA replication within the cell, discontinuous synthesis of DNA does NOT occur in a polymerase chain reaction (PCR). Why?

Lymph is an important body fluid. Choose the INCORRECT statement about the lymph.

Let ' $X$ ' be the perpendicular distance from the centromere of each chromosome to the equatorial plane of a human cell. Which of the following stages of the cell cycle is most likely to have the HIGHEST average value of $X^{\prime}$ ?

Match the features of a plant cell with their corresponding examples

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Osmoreceptors are sensitive to changes in ionic concentrations and volumes of body fluids. Which among the following best describes the function of these osmoreceptors?

Consider the following biomes: Tropical Rainforest $(P)$; Tundra $(Q)$; Desert $(R)$ and Coastal zone $(S)$. The most probable order of Net Primary Productivity of these biomes is

During the CoVID-19 pandemic, SARS-CoV2 virus mutated multiple times giving rise to many variants. What is the genetic material of the SARS-CoV2 virus?

Interneurons play an important role in the execution of spinal cord-mediated reflex action. Where are these interneurons located?

In a cross between individuals of the genotypes PpQQRrSS and ppqqRrSS, what will be the expected number of progenies with the genotype ppQQRrSS in a population of 400 individuals, assuming independent assortment?

Nine percent of a population cannot taste a certain food item because of a recessive allele of the gene IAT. Assuming the population is in Hardy-Weinberg equilibrium, what will be the frequency of dominant and recessive alleles, respectivel...

A single point mutation in gene ' $X$ ' results in breathing difficulty, hypertension as well as partial sterility. Which among the following best explains the observed phenotypes?

In a given species of flowering plant, the colour of the seeds is exclusively determined by the colour of its seed coat. Seed coat colour in this species is governed by a nuclear gene with two alleles. The WHITE ( $W$ ) allele is dominant o...

Shown below are some of the reactions that occur in the metabolic pathway leading to complete oxidation of glucose during aerobic respiration.

i. Pyruvate $\rightarrow$ Acetyl CoA
ii. Dihydroxy acetone phosphate $\rightarrow$ Glyceraldehy...

Which of the following figures CORRECTLY represents the chemiosmotic hypothesis of ATP synthesis occurring in a mitochondrion in a cell? (Keys for the figure; IMS: Intermembrane space, IMM: Inner mitochondrial membrane, MM: Mitochondrial ma...

\(\text {In the following reaction sequence, the major products } M, N \text {, and } O \text { respectively are }\)

Which of the following expressions represents the hydrogen atom wave function $\psi(r)$ shown in the figure below? ( $r$ is the distance of the electron from the nucleus and $a_0$ is a constant)

Identify the correct order of the molecules with respect to the magnitude of their dipole moment:

For the reaction involving ideal gases, $A(g)+2 B(g)=2 C(g)+3 D(g)$, which of the following plots is qualitatively correct? ( $K_p$ and $K_c$ are the equilibrium constants in terms of pressure and concentration respectively. $T$ is the abso...

Benzamide is treated with $\mathrm{Br}_2$ and $\mathrm{NaOH}(\mathrm{aq})$ to form the product $X$, which is then reacted with $\mathrm{NaNO}_2$ and $\mathrm{HCl}(\mathrm{aq})$ at $0-5^{\circ} \mathrm{C}$ to form $Y$. $Y$ is immediately tre...

The products of the reaction between aqueous solutions of $K_4\left[\mathrm{Fe}(\mathrm{CN})_6\right]$ and $\frac{1}{2} \mathrm{H}_2 \mathrm{O}_2$ are

For the colourless complex $\left[M\left(H_2 O\right)_6\right]^{n+}$, where $M$ is a $3 d$ transition metal, the CORRECT ground state $d$-electron configuration of $M$ is

An aqueous solution contains 1.0 M of $\mathrm{X}^{2+}$ and 0.001 M of $\mathrm{Y}^2+$ ions at $25^{\circ} \mathrm{C} . \mathrm{X}^{2+}$ and $\mathrm{Y}^{2+}$ ions do not interact with each other. This solution is put in an electrolytic cel...

\(\text { Which of the following molecules are aromatic? }\)

Which of the following are aryl bromides?

\(\text { The major product } P \text { of the following reaction is }\)

2 g of naphthoic acid (molecular weight $=172 \mathrm{~g} \mathrm{~mol}^{-} 1$ ) dissolved in 20 mL of benzene shows a freezing point depression of 2 K . For benzene, the freezing point depression constant, $K_f=5$ $\mathrm{K} \mathrm{kg} \...

Choose the correct statement about the structure of $\mathrm{C}_{60}$ fullerene

\(\text { The first to fifth ionization energies (IE) of two p-block elements } X \text { and } Y \text { are given below. }\)
$$ \begin{array}{|c|c|c|c|c|c|} \hline & \mathrm{IE}_1(\mathrm{eV}) & \mathrm{IE}_2(\mathrm{eV}) & \mathrm{IE}_...

The van der Waals equation for a real gas is given by $\left(P+\frac{a}{V^2}\right)(V-b)=R T$. What is the dimension of $\left(\frac{a}{b}\right)$ ?

The function given by $f(x)=2 x^3-15 x^2+36 x-5$ is

Let $f(x)=a_n x^n+a_{n-1} x^{n-1}+\cdots+a_1 x+a_0$ be a polynomial. Suppose that $f(0)=0$,
\(\left.\left.\frac{d f}{d x}\right]_{x=0}=1, \frac{d^2 f}{d x^2}\right]_{x=0}=4\)
and
\(\frac{d^3 f}{d x^3}=\frac{d^5 f}{d x^5}\)
Then $f(5)=$

Let $a$ be a nonzero real number and $f: \mathbf{R} \rightarrow \mathbf{R}$ be a continuous function such that $f^{\prime}(x)>0$ for all $x \in R$. Consider $g(x)=f\left(2 a^2 x-a x^2\right)$. Then $g$ has

Consider the tangent lines to the circle $x^2+y^2=1$ at points $P=(1,0)$ and $Q=\left(\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)$. If $R$ is the point of intersection of these two tangent lines, then $\angle P R Q$ is:

Let $\omega$ be a complex root of the quadratic polynomial $x^2+x+1$. The value of

\(\left(\omega+\frac{1}{\omega}\right) \cdot\left(\omega^2+\frac{1}{\omega^2}\right) \cdots\left(\omega^{100}+\frac{1}{\omega^{100}}\right)\)
is

Let $f$ be a continuous function on $[0,1]$ and $F$ be its antiderivative. If $F(0)=1$ and $\int_0^1 f(x) d x=1$, then $F(1)$ is

For a natural number $n$, let $C_n$ be the curve in the $X Y$-plane given by $y=x^n$, where $0 \leq$ $x \leq 1$. Let $A_n$ denote the area of the region bounded between $C_n$ and $C_n+1$. Then the largest value of $A_n$ is

The value of the integral
\(\int_1^{100} \frac{[x]}{x} d x\)
where $[x]$ is the greatest integer less than or equal to $x$ for any real number $x$, is

For arbitrary constants $\alpha, \beta$, the differential equation representing the family of curves $y=$ $(\alpha x+\beta) e^x$ is

Let $A$ be the matrix $\left[\begin{array}{ccc}\cos \theta & 0 & -\sin \theta \\ 1 & 1 & 1 \\ \sin \theta & 0 & \cos \theta\end{array}\right]$. For any natural number $k$, the determinant of $A^k$ is

A randomly chosen card from a deck of 52 cards is given to be a black card (Spade or Club). What is the probability that it is either a face card (King, Queen or Jack) or a Spade?

A lab reports that the global average temperature in the year 2020 was $14.9^{\circ} \mathrm{C}$ and predicts that the global average temperature will increase at the rate of $1 \%$ per year. What will be the global average temperature in t...

Let $X$ be the set of all $2 \times 2$ matrices with real entries and $R \subset X \times X$ be the relation $R=$ $\{(A, B): A B=B A\}$. Which of the following statements is true?

Consider the vectors $\vec{a}=\hat{\imath}+x \hat{\jmath}+2 \hat{k}, \vec{b}=\hat{\imath}+2 \hat{\jmath}+x \hat{k}, \vec{c}=2 \hat{\imath}+\hat{\jmath}+3 \hat{k}$. The values of $x$ for Which there is at least one nonzero vector perpendicul...

Let $S$ be the set of all unit vectors in the $X Y$-plane. Then the set $S$ has

Consider that in a fission of a single Plutonium ( $\mathrm{Pu}^{239}$ ) atom 207 MeV energy is released. Assuming all atoms of Plutonium undergo fission, which of the following options is the closest estimate of the amount of Plutonium req...

In the given circuit each of the resistors is of $1 \mathrm{k} \Omega$ resistance and each of the capacitors has $4 \mu \mathrm{~F}$ capacitance. What is the charge in the capacitor between the points B and F ?

A point mass $m$ attached to a massless string is undergoing circular motion in a vertical plane. The length of the string is $R$ and the acceleration due to gravity is $g$. If the minimum value of the tension in the string is 2 mg , the ma...

In the given circuit, the box $B$ either contains a capacitor, or an inductor or a resistor. The current $I$ versus time $t$ plots for three cases $\left(a_1, a_2, a_3\right)$ are shown in figures. The switch $S$ is closed at time $t=0$. Wh...

The figures in the options show the photocurrent $J$ of a photoelectric material versus the frequency $f$ of an incident light beam. The light beam can have three different intensities $I_1, I_2, I_3$, with $I_3>I_2>$ $I_1$. Which of the op...